Trying to use a query with mongoexport results in an error. But the same query is evaluated by the mongo-client without an error.
In mongo-client:
db
The mongoexport command-line utility supports passing a query in JSON format, but you are trying to evaluate JavaScript in your query.
The JSON format was originally derived from JavaScript's object notation, but the contents of a JSON document can be parsed without eval()ing it in a JavaScript interpreter.
You should consider JSON as representing "structured data" and JavaScript as "executable code". So there are, in fact, two different contexts for the queries you are running.
The mongo command-line utility is an interactive JavaScript shell which includes a JavaScript interpreter as well as some helper functions for working with MongoDB. While the JavaScript object format looks similar to JSON, you can also use JavaScript objects, function calls, and operators.
Your example of 1221029382*1000 is the result of a math operation that would be executed by the JavaScript interpreter if you ran that in the mongo shell; in JSON it's an invalid value for a new Date so mongoexport is exiting with a "Failure parsing JSON string" error.